Neutrons are interesting in that they dump all their energy into a very small region. Instead of losing energy continually and gradually, they travel a ways and then dump all their energy into one spot. This makes them potentially very useful for things like cancer treatment (you can select neutrons to ensure they deliver most of their energy into the cancer, rather than evenly along their travel path). I suspect this effect means that, for reactors, the wear and tear is more localized, but of a larger amplitude.
Not exactly. The initial collisions do indeed cause localised damage cascades, but the overall effect of a large neutron flux is embrittlement of the material. This is a problem already in fission reactor vessels, but the neutron fluxes are a whole order of magnitude larger in fusion reactors, and it's a very difficult problem to solve. To my knowledge, current materials can only just about deal with with the neutron fluxes in standard fission reactors, with no current materials being capable of withstanding neutron fluxes in a fusion reactor over any long (i.e. commercial) timescale at present. It would be a big achievement and a big jump in materials science to discover such a material, completely separate of any fusion project.
(Disclaimer: this is not remotely my field, but I have looked at some of this stuff in the past, and been to talks about ITER.)
Frankly, the best neutron shielding in the world, on a per-cost basis, is water with borax. I don't know why people don't use this more. We used to use stacked bags of borax as neutron shielding when I built a fusion reactor (non-self sustaining, of course), and we had more than enough shielding to handle 2.45 MeV neutrons for under $1000.
A cool thing about the shield being liquid is that you could theoretically replace it while it's running. It could make the neuron shield double as the heat transfer medium too.
Of course I'm a total layman so this is just highlevel blabbering.
Neutrons slow down via interaction with nuclei (all of which except hydrogen are heavier) so they lose energy slowly and scatter all over the place. They have no definite range (search for "fermi age theory" to get a rough idea of the distribution) and can't be meaningfully beamed (unless they are ultra-cold, which is not relevant to fusion power.)
I've made a longer comment above that goes into neutron physics in a little more detail.